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Please help me solve this step by step with wrriten explanation. context and words help me

Please help me solve this step by step with wrriten explanation. context and words-example-1
User Outcoldman
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\begin{gathered} \text{If we try to rationalize} \\ \frac{5}{1+\sqrt[]{7}}\text{ using }\sqrt[]{7} \\ \\ \text{what happens is we still end up having a denominator with a radical} \end{gathered}
\begin{gathered} \frac{5}{1+\sqrt[]{7}}\cdot\frac{\sqrt[]{7}}{\sqrt[]{7}},\text{ multiply by 1} \\ =\frac{5\sqrt[]{7}}{1(\sqrt[]{7})+\sqrt[]{7}(\sqrt[]{7})},\text{ distribute }\sqrt[]{7\text{ }}\text{ to numerators and denominator} \\ =\frac{5\sqrt[]{7}}{\sqrt[]{7}+7}\text{ final answer} \end{gathered}

User Josh Hansen
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